The orthogonal projection of ` vec a\ on\ vec b` is `(( vec adot vec b) vec a)/(|"a"|^2)` b. `(( vec adot vec b) vec b)/(| vec b|^2)` c. ` vec a/(| vec a|)` d. ` vec b/(| vec b|)`

Distance of the point P( vec p) from the line vec r= vec a+lambda vec b is a. |( vec a- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| b. |( vec b- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| c. |( vec a- vec p)+((( vec p- vec b)dot vec b) vec b)/(| vec b|^2)| d. none of these

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

Show that ( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=| [vec a.vec a, vec a.vec b],[ vec a.vec b, vec b.vec b]|

If non-zero vectors vec aa n d vec b are equally inclined to coplanar vector vec c ,t h e n vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec bdot vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec cdot vec a)/(| vec a|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec cdot vec a)/(| vec a|^2) vec a-( vec bdot vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec cdot vec a)/(| vec c|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec cdot vec a)/(| vec c|^2) vec a=( vec bdot vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

Let vec a and vec b be two non-zero perpendicular vectors.A vecrtor vec r satisfying the equation vec r xxvec b=vec a can be vec b-(vec a xxvec b)/(|vec b|^(2)) b.2vec b-(vec a xxvec b)/(|vec b|^(2)) c.|vec a|vec b-(vec a xxvec b)/(|vec b|^(2))d|vec b|vec b-(vec a xxvec b)/(|vec b|^(2))

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If | vec axx vec b|^2=( vec adot vec b)^2=144\ a n d\ | vec a|=4 , find vec bdot

Show that the projection vector vec a and vec b(!=vec 0)( component of vec a aong vec b)is((vec a*vec b)/(|vec b|))vec b

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""xxvec c""= vec b"" xxvec d"",vec a * vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b